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A281301 Trajectory of 1000004999700144385 under the "Reverse and Add!" operation. 8
1000004999700144385, 6834415079694144386, 13668830049399288772, 41457129443403175403, 71914259877895350817, 143719619755790592734, 581014717313707510075, 1151030424627424920260, 1771324671891665221771, 3542550333873429453542, 5996099577656760005995 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

1000004999700144385 is the largest of the first 225 numbers that require exactly 259 steps to turn into a palindrome (see A281390). The sequence reaches a 119-digit palindrome after 259 steps (see b-file). The number was obtained empirically using computer algorithms and was not reported before.

Row 1000004999700144385 of the array in A243238. - Felix Fröhlich, Jan 21 2017

REFERENCES

Popular Computing (Calabasas, CA), The 196 Problem, Vol. 3 (No. 30, Sep 1975).

LINKS

Sergei D. Shchebetov, Table of n, a(n) for n = 0..259

Jason Doucette, World Records

Yutaka Nishiyama, Numerical Palindromes and the 196 Problem, International Journal of Pure and Applied Mathematics, Volume 80, No. 3, 2012, 375-384.

R. Styer, The Palindromic Conjecture and the Fibonacci Sequence, Villanova University, 1986, 1-11.

C. W. Trigg, Palindromes by Addition, Mathematics Magazine, 40 (1967), 26-28.

C. W. Trigg, More on Palindromes by Reversal-Addition, Mathematics Magazine, 45 (1972), 184-186.

Wikipedia, Lychrel Number

196 and Other Lychrel Numbers, 196 and Lychrel Number

Index entries for sequences related to Reverse and Add!

FORMULA

a(n+1) = a(n) + rev(a(n)).

EXAMPLE

a(1) = 1000004999700144385 + 5834410079994000001 = 6834415079694144386.

PROG

(PARI) terms(n) = my(x=1000004999700144385, i=0); while(1, print1(x, ", "); x=x+eval(concat(Vecrev(Str(x)))); i++; if(i==n, break))

/* Print initial 9 terms as follows: */

terms(9) \\ Felix Fröhlich, Jan 21 2017

CROSSREFS

Cf. A023109, A033672, A065198, A065199, A065320, A065321, A065322, A065323, A065324, A065325, A065326, A065327, A070743, A072216, A072217, A072218, A243238, A281390.

Sequence in context: A256312 A173445 A281390 * A286481 A168334 A095434

Adjacent sequences:  A281298 A281299 A281300 * A281302 A281303 A281304

KEYWORD

nonn,base

AUTHOR

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 21 2017

EXTENSIONS

a(9)-a(10) from Felix Fröhlich, Jan 21 2017

STATUS

approved

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Last modified February 22 12:42 EST 2020. Contains 332136 sequences. (Running on oeis4.)